Method and system for image artifact reduction using nearest-neighbor phase correction for echo planar imaging

ABSTRACT

A nearest neighbor phase correction technique is implemented to reduce image artifacts due to phase errors in data acquired in an EPI scan. Image quality for EPI applications, such as DWI, DTI, and fMRI, is improved.

CROSS-REFERENCE TO RELATED APPLICATION

The present invention claims the benefit of U.S. Provisional ApplicationSer. No. 60/615,208 filed Sep. 30, 2004.

BACKGROUND OF THE INVENTION

The present invention relates generally to magnetic resonance (MR)imaging and, more particularly, to a method of image artifact reductionusing nearest-neighbor phase correction.

When a substance such as human tissue is subjected to a uniform magneticfield (polarizing field B₀), the individual magnetic moments of thespins in the tissue attempt to align with this polarizing field, butprecess about it in random order at their characteristic Larmorfrequency. If the substance, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, or “longitudinalmagnetization”, M_(z), may be rotated, or “tipped”, into the x-y planeto produce a net transverse magnetic moment M_(t). A signal is emittedby the excited spins after the excitation signal B₁ is terminated andthis signal may be received and processed to form an image.

When utilizing these signals to produce images, magnetic field gradients(G_(x), G_(y), and G_(z)) are employed. Typically, the region to beimaged is scanned by a sequence of measurement cycles in which thesegradients vary according to the particular localization method beingused. The resulting set of received NMR signals are digitized andprocessed to reconstruct the image using one of many well knownreconstruction techniques.

Echo Planar Imaging (EPI) is used for many MR imaging applications,including Diffusion Weighted Imaging (DWI), Diffusion Tensor Imaging(DTI), and functional Magnetic Resonance Imaging (fMRI), because of itsability to rapidly acquire diagnostic images. Echo Planar Imaging reliesupon bi-polar magnetic gradient fields to acquire MR data. Moreparticularly, EPI is a rapid imaging technique that records an entireimage in a repetition interval or TR period. An EPI pulse sequence isgenerally characterized by a 90° slice selective RF pulse that isapplied in conjunction with a slice selection gradient. An initial phaseencoding gradient pulse and an initial frequency encoding gradient pulseis used to position spins at a corner of k-space, the matrix that isused to define the relative position of acquired signals along a phaseencoding and a frequency encoding direction. A 180° pulse is thenapplied. Typically, this 180° pulse is not slice selective. The phaseand frequency encoding directions are then cycled using phase encodingand readout pulses so as to transverse k-space. In this regard, afrequency encoding gradient follows a phase encoding gradient to recorda time signal. Another phase encoding gradient is then applied followedby a reverse polarity frequency gradient during which another timesignal is recorded. This cycling continues until k-space is filled.Because k-space can be rapidly traversed in this fashion, images can beacquired at a rate tantamount to video rates, e.g. 15–30 images persecond, or faster.

EPI has been successfully used for a number of clinical applications,and is particularly useful in studies involving the human brain. DWI andDTI are imaging sequences that can be used to obtain useful diagnosticinformation, e.g. localization of areas damaged by ischemia orhemorrhagic stroke, creation of anisotropic diffusion coefficient (ADC)maps, enhanced anisotropic diffusion coefficient (eADC) maps, andtractography images.

Another important EPI application is fMRI of the brain. Brain fMRI is animaging technique that relates functional activity occurring in specificlocations of the brain to various stimuli, such as speech, motorfunctions, or visual stimulus. With fMRI it is possible to measuremomentary increases in blood flow to specific thought or motor controlcenters that occur in response to a stimulus. For example, in responseto movement of the right index finger, a rapid momentary increase inblood circulation of the specific part of the brain controlling fingermovement occurs. Such an increase in blood circulation also yields anincrease in oxygen which is paramagnetic and thus affects spin-latticeand spin-spin relaxation times of local brain tissues. These differencesin relaxation times manifest themselves as variations in image contrastand can then be exploited with EPI to measure brain function.

A drawback of EPI is that phase errors that lead to image artifacts whennot removed from the raw data may be introduced during data acquisition.EPI sequences use a single RF pulse followed by multiple dataacquisition windows to encode multiple frames of MR data per RFexcitation. While this speeds the rate of data collection, EPI datacontains phase errors that result in “Nyquist” ghosting in the phaseencoding direction. For a single-shot EPI data collection, Nyquistghosting manifests itself as an artifact resembling the original imageshifted and split in the phase direction.

A number of processes have been developed to correct for these phaseerrors. Known processes are predicated upon the acquisition ofnon-phase-encoded reference data, determining phase errors in thereference data, and correcting phase-encoded data based on the phaseerrors present in the reference data. While these processes have beenfruitful in reducing phase errors in EPI, there still remains a need forfurther improvement in phase error reduction with EPI.

It would therefore be desirable to have a system and method capable ofcorrecting phase errors in EPI acquired MR data to reduce imageartifacts in reconstructed images.

BRIEF DESCRIPTION OF THE INVENTION

The present invention is directed to a process of phase error correctionthat overcomes the aforementioned drawbacks.

The process determines phase errors based on subtracting neighboringframes of non-phase-encoded data collected during a reference scan, anddetermining a first-order fit to the phase of the subtracted data. Thefirst-order fit is then applied to phase-encoded data to reduce phaseerrors in the phase-encoded data. The process is particularly applicableto EPI and EPI-based scanning techniques, such as fMRI, DTI, and DWI.

The present invention is directed to an MR imaging apparatus having aplurality of gradient coils positioned about a bore of a magnet toimpress a polarizing magnetic field and an RF transceiver system and anRF switch controlled by a pulse module to transmit RF signals to an RFcoil assembly to acquire MR images. The apparatus also has a computerprogrammed to acquire frames of reference MR data and characterize eachframe of reference MR data as one of an even reference frame collectedwith positive gradient readout polarity and an odd reference framecollected with negative readout polarity. The computer is alsoprogrammed to determine phase correction coefficients from a phasedifference between adjacent even and odd reference frames, and performan EPI scan to acquire phase-encoded MR data. The computer is furtherprogrammed to apply phase correction to the phase-encoded MR data duringimage reconstruction to reduce image artifacts due to phase errors inthe phase-encoded MR data.

The present invention also includes a method of echo planar imaging. Themethod includes acquiring frames of non-phase-encoded MR data andgenerating a set of phase correction coefficients. The method includestime re-ordering for MR data collected with negative gradient polarity,re-sampling each data frame if data was acquired on a gradient ramp,data apodization, Fourier transformation, and phase computation for eachframe of data. The method further includes computation of phasedifference data from neighboring odd and even frames ofnon-phase-encoded MR data. The method also determines the average phaseterm from the set of phase difference data and then removes this linearphase term from the set of phase difference data. The method alsoincludes determining the phase of the set of phase difference data withthe linear phase term removed to effectively provide phase unwrapping,and summing the average linear phase to the unwrapped phase. The methodthen determines at least one phase correction coefficient from this dataset. The method further includes the steps of acquiring phase-encoded MRdata and applying the at least one phase correction coefficient to thephase-encoded MR data during image reconstruction to reduce imageartifacts due to phase errors in the phase-encoded MR data.

The invention may also be embodied in a computer readable storage mediumhaving a computer program stored thereon and representing a set ofinstructions is disclosed that when executed by a computer causes thecomputer to disable a phase encoding gradient coil assembly and thenacquire odd and even frames of reference MR data. The computer isfurther caused to generate a set of phase difference MR data from phasedifferences between adjacent odd and even frames of reference MR dataand determine at least one phase correction coefficient from the set ofphase difference MR data. The computer is then caused to enable thephase encoding gradient coil assembly and acquire phase-encoded MR data.Phase correction is then applied to the acquired phase-encoded MR dataduring image reconstruction to correct for phase errors in thephase-encoded MR data.

Therefore, in accordance with one aspect of the present invention, anMRI system has a plurality of gradient coils positioned about a bore ofa magnet to impress a polarizing magnetic field and an RF transceiversystem and an RF switch controlled by a pulse module to transmit RFsignals to an RF coil assembly to acquire MR images. The MRI system alsohas a computer programmed to acquire frames of reference MR data andcharacterize each frame of reference MR data as one of an even referenceframe and an odd reference frame. The computer is further programmed todetermine phase correction coefficients from a phase difference betweenadjacent even and odd reference frames and perform an EPI scan toacquire phase-encoded MR data. The computer is also programmed to applyphase correction to the phase-encoded MR data during imagereconstruction to reduce image artifacts due to phase errors in thephase-encoded MR data.

In accordance with another aspect, the invention includes a method ofecho planar imaging that includes the steps of acquiring framesnon-phase-encoded MR data from positive and negative readout gradientpolarities and generating a set of phase difference data fromneighboring frames of non-phase-encoded MR data acquired with positiveand negative readout gradient polarity. The method further includesdetermining an average linear phase term from the set of phasedifference data and removing the average linear phase term from the setof phase difference data. The phase of the set of phase difference datawith the linear phase term removed for phase unwrapping is thendetermined. The method further includes the steps of restoring theaverage linear phase term to the determined phase to yield an unwrappedphase component and determining at least one phase correctioncoefficient from the unwrapped phase component. Phase-encoded MR data isacquired whereby phase correction is applied to the phase-encoded MRdata to reduce phase errors in the phase-encoded MR data.

According to another aspect, the present invention includes a computerreadable storage medium having a computer program stored thereon andrepresenting a set of instructions that when executed by a computercauses the computer to disable a phase encoding gradient coil assembly,and acquire odd and even frames of reference MR data with the phaseencoding gradient coil assembly disabled. The computer is further causedto generate a set of phase difference MR data from phase differencesbetween adjacent odd and even frames of reference MR data and determinea set of phase correction coefficients from the phase difference MRdata. The set of instructions further causes the computer to enable thephase encoding gradient coil assembly and acquire phase-encoded MR data.The set of phase correction coefficients is then applied to the acquiredphase-encoded MR data to correct for phase errors in the phase-encodedMR data.

Various other features, objects and advantages of the present inventionwill be made apparent from the following detailed description and thedrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate one preferred embodiment presently contemplatedfor carrying out the invention.

In the drawings:

FIG. 1 is a schematic block diagram of an MR imaging system for use withthe present invention.

FIG. 2 is a flow chart setting forth the steps an MR data acquisitionand phase correction process in accordance with one embodiment of thepresent invention.

FIG. 3 is a flow chart setting forth the steps of a Variable ReadoutGradient Filtering (VRGF) technique in accordance with anotherembodiment of the present invention.

FIG. 4 is an image of a human brain reconstructed from EPI data acquiredwith a known EPI reconstruction technique.

FIG. 5 is an image of the same human brain as shown in FIG. 4reconstructed from EPI data acquired with the data acquisition and phasecorrection process illustrated in FIG. 2 and the VRGF re-samplingtechnique illustrated in FIG. 3.

FIG. 6 is a flow chart setting forth the steps of an EPI reconstructionutilizing VRGF re-sampling with shifted/re-aligned reference data inaccordance with another embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, the major components of a preferred magneticresonance imaging (MRI) system 10 incorporating the present inventionare shown. The operation of the system is controlled from an operatorconsole 12 which includes a keyboard or other input device 13, a controlpanel 14, and a display screen 16. The console 12 communicates through alink 18 with a separate computer system 20 that enables an operator tocontrol the production and display of images on the display screen 16.The computer system 20 includes a number of modules which communicatewith each other through a backplane 20 a. These include an imageprocessor module 22, a CPU module 24 and a memory module 26, known inthe art as a frame buffer for storing image data arrays. The computersystem 20 is linked to disk storage 28 and tape drive 30 for storage ofimage data and programs, and communicates with a separate system control32 through a high speed serial link 34. The input device 13 can includea mouse, joystick, keyboard, track ball, touch activated screen, lightwand, voice control, or any similar or equivalent input device, and maybe used for interactive geometry prescription.

The system control 32 includes a set of modules connected together by abackplane 32 a. These include a CPU module 36 and a pulse generatormodule 38 which connects to the operator console 12 through a seriallink 40. It is through link 40 that the system control 32 receivescommands from the operator to indicate the scan sequence that is to beperformed. The pulse generator module 38 operates the system componentsto carry out the desired scan sequence and produces data which indicatesthe timing, strength and shape of the RF pulses produced, and the timingand length of the data acquisition window. The pulse generator module 38connects to a set of gradient amplifiers 42, to indicate the timing andshape of the gradient pulses that are produced during the scan. Thepulse generator module 38 can also receive patient data from aphysiological acquisition controller 44 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes attached to the patient. And finally, the pulsegenerator module 38 connects to a scan room interface circuit 46 whichreceives signals from various sensors associated with the condition ofthe patient and the magnet system. It is also through the scan roominterface circuit 46 that a patient positioning system 48 receivescommands to move the patient to the desired position for the scan.

The gradient waveforms produced by the pulse generator module 38 areapplied to the gradient amplifier system 42 having Gx, Gy, and Gzamplifiers. Each gradient amplifier excites a corresponding physicalgradient coil in a gradient coil assembly generally designated 50 toproduce the magnetic field gradients used for spatially encodingacquired signals. The gradient coil assembly 50 forms part of a magnetassembly 52 which includes a polarizing magnet 54 and a whole-body RFcoil 56. A transceiver module 58 in the system control 32 producespulses which are amplified by an RF amplifier 60 and coupled to the RFcoil 56 by a transmit/receive switch 62. The resulting signals emittedby the excited nuclei in the patient may be sensed by the same RF coil56 and coupled through the transmit/receive switch 62 to a preamplifier64. The amplified MR signals are demodulated, filtered, and digitized inthe receiver section of the transceiver 58. The transmit/receive switch62 is controlled by a signal from the pulse generator module 38 toelectrically connect the RF amplifier 60 to the coil 56 during thetransmit mode and to connect the preamplifier 64 to the coil 56 duringthe receive mode. The transmit/receive switch 62 can also enable aseparate RF coil (for example, a surface coil) to be used in either thetransmit or receive mode. System 10 may also be equipped with a phasedarray coil for parallel acquisitions.

The MR signals picked up by the RF coil 56 are digitized by thetransceiver module 58 and transferred to a memory module 66 in thesystem control 32. A scan is complete when an array of raw k-space datahas been acquired in the memory module 66. This raw k-space data isrearranged into separate k-space data arrays for each image to bereconstructed, and each of these is input to an array processor 68 whichoperates to Fourier transform the data into an array of image data. Thisimage data is conveyed through the serial link 34 to the computer system20 where it is stored in memory, such as disk storage 28. In response tocommands received from the operator console 12, this image data may bearchived in long term storage, such as on the tape drive 30, or it maybe further processed by the image processor 22 and conveyed to theoperator console 12 and presented on the display 16.

The present invention is directed to a process of image reconstructionof EPI raw data that may be carried out with the MR imaging systemillustrated in FIG. 1, or equivalent thereof. Frames of reference scandata are collected prior to an EPI scan and processed to determine a setof constant and linear phase correction coefficients for each frame ofdata. The new phase correction coefficients are then used to removephase errors included with the EPI MR raw data to reduce imageartifacts. Extensive testing with both 1.5 T and 3.0 T MR systems hasshown significant benefit of the present invention. While the inventionwill be described with respect to steps of a process or method, oneskilled in the art will readily appreciate the present invention may beembodied in instructions of a computer program that when executed by acomputer carries out the phase error correction processes describedherein.

Referring now to FIG. 2, the steps of an MR data acquisition process areillustrated. Process 70 is designed to acquire non-phase-encoded MRdata, determine phase correction coefficients from the non-phase-encodedor reference MR data, and then apply the phase error correctioncoefficients to acquired phase-encoded MR data during imagereconstruction to reduce image artifacts arising from phase errors.Process 70 is particularly well-suited for EPI scans which typicallyemploy a phase error correction, but may also be applicable with otherscan protocols. Additionally, process 70 may be used for single-shot aswell as multi-shot MR data acquisitions.

Process 70 begins at 72 with the prescription of an EPI scan, such asfMRI acquisition, and positioning of the subject for scanning. Prior toacquiring imaging data, reference data is acquired. This reference datais acquired without phase encoding. As such, the gradient coil assemblyresponsible for phase encoding is disabled at 74 whereupon the EPIacquisition of non-phase encoding data is initiated at 76. It iscontemplated that a number of EPI pulse sequences may be used for theacquisition of the non-phase-encoded reference data. Additionally, it ispreferred that the reference data is collected with the same measurementparameters that will used to acquire phase-encoded imaging data.

Consistent with the applied EPI scan, frames or k-space rows ofreference data is acquired at 78. The frames are then segmented into oddand even frames 80 corresponding to whether the frames were collectedwith positive readout gradient polarity (odd) or negative readoutgradient polarity (even). In this regard, each frame or row of k-spaceis designated as either an odd row or an even row. Further, forsingle-shot EPI, k-space is constructed to have alternating odd and evenrows. Once the ramp-sampled EPI MR data has been acquired in step 78,frames of MR raw data collected with negative gradient polarity must betime-reversed. In this regard, VRGF re-sampling is not performed on thenon-phase-encoded EPI reference data. Next, the Fourier transform ofeach row of k-space is performed. After the Fourier transform, the phaseof each element in k-space may be computed. A phase difference data setis then generated. For single-shot EPI this is done by subtractingadjacent odd and even rows of MR phase data. For multiple-shot EPI,adjacent frames of MR raw data in k-space acquired with the samegradient polarity are averaged together to form a reduced set of Mframes of data from which phase difference data sets will be generated.Specifically, the phase difference dataset is generated at 82 bysubtracting the phase of adjacent odd-even frames or rows of k-space.For M frames of data, M−1 rows of phase difference data is generated.Phase subtraction may be implemented by multiplying each frame by thecomplex conjugate of the next frame as indicated in Eqn. 1:pdiff _(m) [n]=r _(m) [n]*r* _(m+1) [n] for n=0,1, . . . ,N−1 and m=0,1,. . . ,M−2  (Eqn. 1),with the phase difference between adjacent rows defined by:

$\begin{matrix}{{\phi_{m}\lbrack n\rbrack} = {{\arctan\;\left( \frac{{Re}\left( {{pdiff}_{m}\lbrack n\rbrack} \right)}{{Im}\left( {{pdiff}_{m}\lbrack n\rbrack} \right)}\; \right)\mspace{14mu}{for}\mspace{14mu} n} = {\quad{0,1,\cdots\mspace{11mu},\mspace{14mu}{{N - {1\mspace{14mu}{and}\mspace{14mu} m}} = 0},1,\cdots\mspace{11mu},\mspace{14mu}{M - 2},}\;}}} & \left( {{Eqn}.\mspace{14mu} 2} \right)\end{matrix}$and the magnitude of the nearest neighbor subtraction given by:ρ_(m) [n]=|pdiff _(m) [n]| for n=0,1, . . . ,N−1 and m=0,1, . . .,M−2  (Eqn. 3).

From the phase difference dataset, a linear phase term is determined at84. This linear phase term is computed by summing all real values in thephase difference dataset and all imaginary values in the phasedifference dataset, then taking the arctangent to compute the phase, asset forth in Eqn. 4:

$\begin{matrix}{\phi_{ahn} = {\arctan\;{\left( \frac{{Re}\;\left( {\sum\limits_{m = 0}^{M - 2}\;{\sum\limits_{n = 0}^{N - 2}\;{{{pdiff}_{m}\lbrack n\rbrack} \star {{pdiff}_{m}^{*}\left\lbrack {n + 1} \right\rbrack}}}} \right)}{{Im}\left( {\sum\limits_{m = 0}^{M - 2}\;{\sum\limits_{n = 0}^{N - 2}\;{{{pdiff}_{m}\lbrack n\rbrack} \star {{pdiff}_{m}^{*}\left\lbrack {n + 1} \right\rbrack}}}} \right)} \right).}}} & \left( {{Eqn}.\mspace{14mu} 4} \right)\end{matrix}$

The linear phase term, as determined from Eqn. 4, is then subtractedfrom the phase difference dataset at 86 as follows. Given:

$\begin{matrix}{{{{ramp}\lbrack n\rbrack} = {{n - {\frac{N}{2}\mspace{14mu}{for}\mspace{14mu} n}} = 0}},1,\cdots\mspace{11mu},\mspace{14mu}{N - 1},{and}} & \left( {{Eqn}.\mspace{14mu} 5} \right) \\{{{\phi_{{ahn}_{-}{row}}\lbrack n\rbrack} = {{\phi_{ahn} \star {{{ramp}\lbrack n\rbrack}\mspace{14mu}{for}\mspace{14mu} N}} = 0}},1,\cdots\mspace{11mu},\mspace{14mu}{N - 1},} & \left( {{Eqn}.\mspace{14mu} 6} \right)\end{matrix}$then the linear phase component can be removed for each row (m) by:ψ_(m) [n]=φ _(m) [n]−φ _(ahn) _(—) _(row) [n] for n=0,1, . . . ,N−1 andm=0,1, . . . ,M−2  (Eqn. 7).

With the linear phase component removed from each row of the phasedifference dataset 86, the phase of the phase difference dataset is thenrecalculated, or otherwise re-determined, at 88 to perform phaseunwrapping. The phase of the phase difference dataset with the removedlinear phase component may be defined by:

$\begin{matrix}{{{\psi_{m}\lbrack n\rbrack} = {{{\tan^{- 1}\left( \frac{\cos\;\left( {\psi_{m}\lbrack n\rbrack} \right)}{\sin\;\left( {\psi_{m}\lbrack n\rbrack} \right)} \right)}\mspace{14mu}{for}\mspace{14mu} n} = 0}},1,\ldots\mspace{11mu},\mspace{14mu}{{N - {1\mspace{14mu}{and}\mspace{14mu} m}} = 0},1,\cdots\mspace{11mu},\mspace{14mu}{M - 2.}} & \left( {{Eqn}.\mspace{14mu} 8} \right)\end{matrix}$

After step 88, the phase will be defined by:−π≦ψ_(m) [n]≦π for n=0,1, . . . ,N−1 and m=0,1, . . . ,M−2  (Eqn. 9).

In a preferred embodiment of the invention, process 90 restores thelinear phase component prior to a weighted least-squares fit. In thisregard:ψ_(m) [n]=ψ _(m) [n]+φ _(ahn) _(—) _(row) [n] for n=0,1, . . . ,N−1 andm=0,1, . . . ,M−2  (Eqn. 10).

As referenced above, the present invention employs a weightedleast-squares fit to provide a first-order characterization of phaseerrors occurring during EPI reference scan data acquisition in order toremove phase errors in EPI acquired scan data. As such, following step90, phase correction coefficients for the weighted least-squares fit aredetermined at 92 for each row or frame of the phase difference dataset.In this regard, a first-order fit is determined by:ψ_(m) [n]=(a _(m)*ramp[n])+b _(m)+ε_(m) for n=0,1, . . . ,N−1 and m=0,1,. . . ,M−2  (Eqn. 11),where ε_(m) is the error term (minimized using a weighted least squarestechnique) determined from the unwrapped phase difference, ψ_(m)[n], asdetermined from Eqn. (10), and the magnitude of the nearest neighborsubtraction, ρ_(m)[n], as determined from Eqn. (3).

The phase correction coefficients are interpolated from the results ofthe weighted least-squares fit of the phase difference data. Given thatthere are only M-1 rows of phase difference data, the first and the lastrow of phase difference coefficients are duplicated to form a set of M-1coefficients. Specifically:α₀=a₀α_(m+1) =a _(m) for m=0,1, . . . ,M−2α_(M)=a_(M−2)  (Eqn. 12);β₀=b₀β_(m+1) =b _(m) for m=0,1, . . . ,M−2β_(M)=B_(M−2)  (Eqn. 13).This set of linear (α_(m)) and constant (β_(m)) coefficients can then besmoothed at 94 using one of a number of smoothing functions. In thepreferred embodiment, an infinite impulse response (IIR) type filterwith quadratic smoothing properties is used, however other conventionalsmoothing filters maybe used.

Following smoothing of the linear and constant correction coefficientsat 94, linear and constant phase correction coefficients are determinedfor each row of the phase difference dataset at 96. The linear phasecorrection coefficients for each row are determined by:

$\begin{matrix}{{{lin}_{m} = {{\left( {- 1^{m}} \right)\frac{\alpha_{m} + \alpha_{m + 1}}{2}\mspace{14mu}{for}\mspace{14mu} m} = 0}},1,\cdots\mspace{11mu},\mspace{14mu}{M - 1},} & \left( {{Eqn}.\mspace{14mu} 14} \right)\end{matrix}$and the constant phase correction coefficients are determined by:

$\begin{matrix}{{{con}_{m} = {{\left( {- 1^{m}} \right)\frac{\beta_{m} + \beta_{m + 1}}{2}\mspace{14mu}{for}\mspace{14mu} m} = 0}},1,\cdots\mspace{11mu},\mspace{14mu}{M - 1.}} & \left( {{Eqn}.\mspace{14mu} 15} \right)\end{matrix}$

The determined linear and constant phase correction coefficients arethen stored in volatile memory and saved to computer storage media to beused to correct phase-encoded EPI data prior to image reconstruction.

Following determination of the phase correction coefficients, process 70continues with enablement of the phase encoding gradient coil assemblyat 100. In this regard, during EPI imaging data acquisition,phase-encoded MR data is acquired at 102. Once the ramp-sampled EPI MRdata has been acquired in step 102, frames of MR raw data collected withnegative gradient polarity must be time-reversed. Then, phase correctionis performed on the ramp-sampled data by first performing a Fouriertransformation on the ramp-sampled data 104. After the Fourier transform104, phase correction is applied 106 to adjust the phase for each datapoint in the row in accordance with Eqns. 16–18 below:χ[n]=(ramp[n]·lin _(m))+con _(m) for n=0,1, . . . ,N−1; m=0,1, . . . ,M−1  (Eqn. 16),phase_(—) corr _(m) [n]=cos(χ[n])+i sin(χ[n])  (Eqn. 17), andr _(m) _(—) _(corrected) [n]=r _(m) [n]·phase_(—) corr[n]  Eqn. (18).

By applying phase correction during image reconstruction, the phase ofeach data point in the row is adjusted in such a manner as to reduceartifacts in the image resulting from phase errors. This phaseadjustment is continued for each row of the row transformed data. Thephase corrected data (after Eqn. 18) undergoes a subsequent inverseFourier transformation to return the data to the time domain 108. Then,VRGF re-sampling is performed 109 after phase correction for each row ofMR data. Next, each row of MR data is Fourier transformed 110 in theconventional manner. After all rows have been Fourier transformed 110,each column undergoes a Fourier transform 111 whereupon an image isreconstructed and displayed at 112, and process 70 ends at 113.

In addition to the phase error correction technique described withrespect to the process of FIG. 2, the present invention is also directedto a VRGF re-sampling technique also designed to improve image qualityduring EPI reconstruction. VRGF re-sampling is a time domain dependentinterpolation process that is carried out to re-sample raw datacollected with variable readout gradients (ramp-sampling). VRGFre-sampling typically uses discrete-time convolution to transform dataacquired during gradient transitions into uniformly sampled data typicalof that acquired during gradient steady-state. Moreover, VRGFre-sampling is conventionally applied before phase correction. As aresult, phase errors that are present in the raw, acquired MR data maynot be suitable for phase correction. These phase errors areparticularly well-pronounced when EPI data is acquired with poorlycalibrated MR systems. Notwithstanding the advantages achieved withconventional VRGF re-sampling, performing phase correction before VRGFre-sampling can be error prone, and is generally inefficient if a systemis not calibrated sufficiently to provide proper echo alignment betweendata collected with positive and negative readout gradient polarity.Accordingly, the present invention is also directed to an EPIreconstruction technique whereby phase correction occurs before VRGFre-sampling to make phase correction less sensitive to echo alignmentdeficiencies that may exist in a poorly calibrated system.

Referring now to FIG. 3, process 114 sets forth the steps of an EPIreconstruction technique in accordance with another embodiment of theinvention. Process 114 begins at 115 with the prescription of an EPIscan. Reference, non-phase-encoded, ramp-sampled MR data is thenacquired at 116 in a manner similar to that described with respect toFIG. 2. Bandpass asymmetry correction may then be performed at 118 tocorrect for the effects of asymmetrical filter response on the MR data.The bandpass asymmetry corrected data is then row Fourier transformed(without re-sampling) 120 and phase correction coefficients aredetermined, or otherwise calculated, at 122. The phase correctioncoefficients are preferably determined in accordance with the techniquedescribed above with respect to FIG. 2 and Eqns. 1–18. The determinedphase correction coefficients are then stored in memory and saved tocomputer media at 124 and will be used for phase correction during EPIreconstruction.

After the phase correction coefficients have been determined and stored,phase-encoded, ramp-sampled EPI data is acquired at 126 consistent withthe parameters of the MR session defined at 114. Similar to the acquiredreference data, the EPI data may also be bandpass asymmetry corrected ina conventional manner to correct for asymmetries at 128. The MR raw datais then Fourier transformed and the stored phase correction coefficientsare then applied to the data 130. The phase correction coefficients areapplied to reduce phase errors that are typically encountered duringEPI. Next, the phase corrected data is then inverse Fourier transformed,completing the phase correction step 130.

After the step of phase correction 130, the phase corrected data issubjected to VRGF re-sampling. The phase corrected data is re-sampledusing one of a number of known VRGF re-sampling techniques. There-sampled data is then row and column Fourier transformed at 134 and136, respectively, to reconstruct an image at 138, whereupon process 112ends. As described above and in contrast to known EPI reconstructionprocesses, VRGF re-sampling is carried out after phase correction. Inthis regard, phase errors in the raw data are reduced prior tore-sampling. This is especially evident for poorly calibrated systemswhere echo alignment between frames of data collected with positive andnegative gradient readout polarity varies significantly.

The robustness of the phase correction and VRGF re-ordering processesdescribed with respect to FIGS. 2 and 3 is illustrated in the images ofFIGS. 4 and 5. FIGS. 4 and 5 correspond to images acquired of a phantomfrom data acquired with a single shot EPI scan having an echo time (TE)of 50 milliseconds, a TR of 2000 milliseconds, a field-of-view (FOV) of24 centimeters, a slice thickness of 5 millimeters, a 64×64 k-spacematrix, 1 NEX, and ramp sampling. FIG. 4 is an image that illustratesthe edge ghosting and other phase error artifacts that can beexperienced using conventional EPI reconstruction techniques. FIG. 5, onthe other hand, is an image reconstructed from EPI data acquired, phasecorrected, and re-sampled consistent with the processes described withrespect to FIGS. 2 and 3. As shown, in the image of FIG. 5 the ghostingpresent in the image of FIG. 4 has been removed. Thus, the image of FIG.5 has better image quality when compared to the image of FIG. 4.

A drawback of post-phase correction VRGF re-sampling, however, is thatthe Fourier transform must be performed on a larger dataset. Then, afterphase correction, an inverse Fourier transform must be carried out sothat the VRGF re-sampling can be performed in the time domain. As aresult, the computational requirements of the process can be burdensome.In this regard, the present invention is also directed to an EPIreconstruction technique that performs VRGF before phase correction in aconventional manner, but also reduces phase errors to a degree notfeasible with conventional EPI reconstruction techniques.

Referring now to FIG. 6, process 140 begins at 142 with the prescriptionof an EPI scan to acquire ramp-sampled MR data from a subject, such as abrain image using fMRI. Prior to the acquisition of imaging data,reference data that lacks phase encoding is acquired at 144. Phasecorrection coefficients are then determined at 145 in accordance withthe phase correction coefficient determination process described withrespect to FIG. 2 and Eqns. 1–18 with no VRGF re-sampling applied to theMR data. The phase correction coefficients are then used to determineappropriate shift parameters. Specifically, the linear phase correctioncoefficients for all views (frames or rows) of data collected withnegative polarity gradients are averaged together to yield an averagelinear phase correction term for negative views, γ_(n). Similarly, thelinear phase correction coefficients for all views of data acquired withpositive polarity gradients are averaged together to form an averagelinear phase correction term for positive views, γ_(p). The γ_(n) andγ_(p) parameters are used to determine the appropriate amount ofshifting in the time domain to be done on the raw data prior to EPIreconstruction for frames of data collected with negative and positivepolarity gradients, respectively. The odd and even frames of referencedata are then shifted at 146 based on the γ_(n) and γ_(p) parameters asshown below.γ_(p)∝δ_(p)γ_(n)∝δ_(n)

where {δ_(p)δ_(n)} are integers.

For negative gradient readout polarity:

$\begin{matrix}{{k_{m}\lbrack n\rbrack} = {{\begin{Bmatrix}{{{k_{negative}\left\lbrack {n + \delta_{n}} \right\rbrack}\mspace{14mu}{for}\mspace{14mu} 0} \leq {n + \delta_{n}} < N} \\{0\mspace{14mu}{otherwise}}\end{Bmatrix}\mspace{14mu}{for}\mspace{14mu} 0} \leq n < {N.}}} & \left( {{Eqn}.\mspace{14mu} 19} \right)\end{matrix}$

For positive gradient readout polarity:

$\begin{matrix}{{k_{m}\lbrack n\rbrack} = {{\begin{Bmatrix}{{{k_{positive}\left\lbrack {n + \delta_{p}} \right\rbrack}\mspace{14mu}{for}\mspace{14mu} 0} \leq {n + \delta_{p}} < N} \\{0\mspace{14mu}{otherwise}}\end{Bmatrix}\mspace{14mu}{for}\mspace{14mu} 0} \leq n < {N.}}} & \left( {{Eqn}.\mspace{14mu} 20} \right)\end{matrix}$

A second pass is then made through the reference data whereupon theshifted data is then bandpass asymmetry corrected at 148 to correct forasymmetries followed by VRGF re-sampling 150. In this regard, VRGFre-sampling takes place prior to phase correction, but is applied totime-shifted or re-aligned raw data. Shifting the data effectivelyperforms crude echo alignment between data frames collected withpositive and negative gradient polarity. The re-sampled data is then rowFourier transformed 152 and new phase correction coefficients aredetermined at 154. Preferably, the new phase correction coefficients aredetermined in accordance with the steps described with respect to FIG. 2and Eqns. 1–18. The new phase correction coefficients are then stored involatile memory and saved to computer storage media at 156 forsubsequent use during EPI reconstruction.

Once the new phase correction coefficients have been determined,phase-encoded EPI data is acquired at 158. The phase-encoded data isthen bandpass asymmetry corrected to correct for asymmetries at 160.VRGF re-sampling is then carried out to re-sample data acquired duringgradient transitions. The re-sampled data is then row Fouriertransformed at 164 followed by application of the phase correctioncoefficients at 166 to correct for phase errors in the phase-encoded EPIdata. Following phase correction, an image is reconstructed anddisplayed (and/or stored) in a conventional manner at 168, whereupon theprocess ends at 170.

The present invention is applicable to single and multi-channelreconstruction where data from each channel is processed independentlyand then combined using a sum of the squares technique. The presentinvention may also be carried out for multi-channel parallel imagingtechniques, such as SENSetivity Encoding (SENSE) or Array Spatial andSensitivity Encoding Technique (ASSET). The present invention is alsoapplicable with EPI scans carried out at several magnetic fieldstrengths, including, but not limited to 1.5 and 3.0 Tesla.

Moreover, it is contemplated that the non-phase-encoded MR referencedata can be acquired with a multiple channel phased array coil and phasecorrection coefficients be determined for each channel. These phasecorrection coefficients are then applied to the same channel duringimage reconstruction of the phase-encoded data. Additionally, it iscontemplated that phase correction coefficients could be determined foronly one channel, and then phase correction coefficients from thatchannel are applied to all channels of data during image reconstructionof the phase-encoded data. In yet another embodiment, thenon-phase-encoded MR reference data is acquired from one slice locationand the phase correction coefficients are determined for only one slicelocation. In this regard, the phase correction coefficients determinedfrom the one slice are applied to the multiple slices during imagereconstruction of the phase-encoded data. In yet another embodiment, thenon-phase-encoded MR reference data is acquired from multiple slicelocations and the phase correction coefficients are determined for eachslice location. The phase correction coefficients are then applied tothe same slice location during image reconstruction of the phase-encodeddata.

Therefore, the present invention includes an MR imaging apparatus havinga plurality of gradient coils positioned about a bore of a magnet toimpress a polarizing magnetic field and an RF transceiver system and anRF switch controlled by a pulse module to transmit RF signals to an RFcoil assembly to acquire MR images. The apparatus also has a computerprogrammed to acquire frames of reference MR data and characterize eachframe of reference MR data as one of an even reference frame and an oddreference frame. The computer is also programmed to determine phasecorrection coefficients from a phase difference between adjacent evenand odd reference frames. The computer is further programmed to performan EPI scan to acquire phase-encoded MR data and to apply phasecorrection to the phase-encoded MR data during image reconstruction toreduce phase errors in the phase-encoded MR data.

The present invention also includes a method of echo planar imaging. Themethod includes acquiring a set of non-phase-encoded MR data andgenerating a set of phase difference data from the non-phase-encoded MRdata. The method also determines the average phase term from the set ofphase difference data and then removes this linear phase term from theset of phase difference data. The method also includes determining thephase of the set of phase difference data with the linear phase termremoved to effectively provide phase unwrapping, and summing the averagelinear phase to the unwrapped phase. The method then determines at leastone phase correction coefficient from this data set. The method furtherincludes the steps of acquiring phase-encoded MR data and applying phasecorrection to the phase-encoded MR data during image reconstruction toreduce image artifacts due to phase errors in the phase-encoded MR data.

A computer readable storage medium having a computer program storedthereon and representing a set of instructions is also disclosed thatwhen executed by a computer causes the computer to disable a phaseencoding gradient coil assembly and then acquire odd and even frames ofreference MR data with the phase encoding gradient coil assemblydisabled. The computer is further caused to generate a set of phasedifference MR data from phase differences between adjacent odd and evenframes of reference MR data and determine at least one phase correctioncoefficient from the set of phase difference MR data. The computer isthen caused to enable the phase encoding gradient coil assembly andacquire phase-encoded MR data. Then phase correction is applied to theacquired phase-encoded MR data during image reconstruction to correctfor phase errors in the phase-encoded MR data.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

1. A magnetic resonance imaging (MRI) system comprising: a plurality ofgradient coils positioned about a bore of a magnet to impress apolarizing magnetic field and an RF transceiver system and an RF switchcontrolled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR images; and a computer programmed to: acquireframes of reference MR data; characterize each frame of reference MRdata as one of an even reference frame and an odd reference frame;determine phase correction coefficients from a phase difference betweenadjacent even and odd reference frames; perform an EPI scan to acquirephase-encoded MR data; and apply phase correction to the phase-encodedMR data during image reconstruction to reduce image artifacts due tophase errors in the phase-encoded MR data.
 2. The MRI system of claim 1wherein the phase-encoded MR data includes rows of MR data and whereinthe phase correction coefficients include a constant term and a linearterm for each row of MR data.
 3. The MRI system of claim 1 wherein thecomputer is further programmed to apply a first-order phase correctionto the phase-encoded MR data during image reconstruction.
 4. The MRIsystem of claim 3 wherein the computer is further programmed todetermine the phase correction coefficients from non-phase-encoded databy subtracting the phase of adjacent odd and even frames to generate aset of phase difference data, and determining the phase correctioncoefficients from the set of phase difference data.
 5. The MRI system ofclaim 4 wherein the computer is further programmed to determine anaverage linear phase of the set of phase difference data by: summing allreal values and all imaginary values in the set of phase differencedata; and taking an arctangent of a ratio of the sum of all real valuesto the sum of all imaginary values.
 6. The MRI system of claim 5 whereinthe computer is further programmed to subtract the average linear phaseterm from each term of the set of phase-difference data.
 7. The MRIsystem of claim 6 wherein the computer is further programmed todetermine a phase of the set of phase-difference data with averagelinear phase removed to effectively provide phase unwrapping.
 8. The MRIsystem of claim 7 wherein the computer is further programmed to re-storethe removed average linear phase of the phase difference data prior to aweighted least-squares fit to obtain a first-order characterization ofphase for each row of phase-difference data.
 9. The MRI system of claim4 wherein the computer is further programmed to determine a weightedfirst-order fit with a linear and a constant term for each row of theset of phase-difference data.
 10. The MRI system of claim 9 wherein thecomputer is further programmed to interpolate the phase correctioncoefficients from the first-order fit.
 11. The MRI system of claim 9wherein the computer is further programmed to smooth the phasecorrection coefficients prior to applying the phase correctioncoefficients to the phase-encoded MR data.
 12. The MRI system of claim 1wherein the magnet is one of a 1.5T and a 3T magnet.
 13. A method ofecho planar imaging comprising the steps of: acquiring framesnon-phase-encoded MR data from positive and negative readout gradientpolarities; generating a set of phase difference data from neighboringframes of non-phase-encoded MR data acquired with positive and negativereadout gradient polarity; determining an average linear phase term fromthe set of phase difference data; removing the average linear phase termfrom the set of phase difference data; determining the phase of the setof phase difference data with the linear phase term removed for phaseunwrapping; restoring the average linear phase term to the determinedphase to yield an unwrapped phase component; determining at least onephase correction coefficient from the unwrapped phase component;acquiring phase-encoded MR data; and applying phase correction to thephase-encoded MR data to reduce phase errors in the phase-encoded MRdata.
 14. The method of claim 13 wherein the computer is furtherprogrammed to acquire the frames of non-phase-encoded MR data inreal-time with the phase-encoded MR data.
 15. The method of claim 14further comprising the step of segmenting the frames ofnon-phase-encoded MR data into odd reference frames and even referenceframes.
 16. The method of claim 15 wherein an even reference frame isadjacent to an odd reference frame with opposite readout gradientpolarity.
 17. The method of claim 16 wherein the step of determining theaverage linear phase term includes summing all real values and allimaginary values of the set of phase difference data and determining anarctangent of a ratio of the sum of real values to the sum of imaginaryvalues.
 18. The method of claim 13 further comprising the step ofre-sampling acquired phase-encoded MR data acquired during gradienttransitions after phase correction of the phase-encoded MR data.
 19. Themethod of claim 13 further comprising the step of acquiring the MR datawith a phased array coil assembly configured for parallel imaging. 20.The method of claim 13 further comprising the step of acquiring thephase-encoded MR data with an EPI scan.
 21. The method of claim 13further comprising the step of acquiring the non-phase-encoded MRreference data with a multiple channel phased array coil and computingphase correction coefficients for each channel, and then applying thesephase correction coefficients to the same channel during imagereconstruction of the phase-encoded data.
 22. The method of claim 13further comprising the step of acquiring the non-phase-encoded MRreference data with a multiple channel phased array coil and computingphase correction coefficients for only one channel, then applying thephase correction coefficients from that channel to all channels duringimage reconstruction of the phase-encoded data.
 23. The method of claim13 further comprising the step of acquiring the non-phase-encoded MRreference data from multiple slice locations and computing phasecorrection coefficients for each slice location, and then applying thesephase correction coefficients to the same slice location during imagereconstruction of the phase-encoded data.
 24. The method of claim 13further comprising the step of acquiring the non-phase-encoded MRreference data from one slice location and computing phase correctioncoefficients for only one slice location, then applying these phasecorrection coefficients to multiple slice locations during imagereconstruction of the phase-encoded data.
 25. A computer readablestorage medium having a computer program stored thereon and representinga set of instructions that when executed by a computer causes thecomputer to: disable a phase encoding gradient coil assembly; acquireodd and even frames of reference MR data with the phase encodinggradient coil assembly disabled; generate a set of phase difference MRdata from phase differences between adjacent odd and even frames ofreference MR data; determine a set of phase correction coefficients fromthe phase difference MR data; enable the phase encoding gradient coilassembly; acquire phase-encoded MR data; and apply the set of phasecorrection coefficients to the acquired phase-encoded MR data to correctfor phase errors in the phase-encoded MR data.
 26. The computer readablestorage medium of claim 25 wherein the set of instructions furthercauses the computer to acquire the phase-encoded MR data with an EPIreadout.
 27. The computer readable storage medium of claim 25 whereinthe set of instructions further causes the computer to determine afirst-order polynomial fit to the set of phase difference MR data andapply phase correction coefficients derived therefrom to thephase-encoded MR data.
 28. The computer readable storage medium of claim27 wherein the set of instructions further causes the computer todetermine a constant phase correction coefficient and a linear phasecorrection coefficient for each k-space row of phase difference MR data.